Integral Geometry And Geometric Probability


Integral Geometry And Geometric Probability
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Integral Geometry And Geometric Probability


Integral Geometry And Geometric Probability
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Author : Luis A. Santaló
language : en
Publisher: Cambridge University Press
Release Date : 2004-10-28

Integral Geometry And Geometric Probability written by Luis A. Santaló and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-28 with Mathematics categories.


Classic text on integral geometry now available in paperback in the Cambridge Mathematical Library.



Integral Geometry And Geometric Probability


Integral Geometry And Geometric Probability
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Author : Luis Antonio Santaló
language : en
Publisher:
Release Date : 1984

Integral Geometry And Geometric Probability written by Luis Antonio Santaló and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Geometric probabilities categories.




Introduction To Geometric Probability


Introduction To Geometric Probability
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Author : Daniel A. Klain
language : en
Publisher: Cambridge University Press
Release Date : 1997-12-11

Introduction To Geometric Probability written by Daniel A. Klain and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-12-11 with Mathematics categories.


The purpose of this book is to present the three basic ideas of geometrical probability, also known as integral geometry, in their natural framework. In this way, the relationship between the subject and enumerative combinatorics is more transparent, and the analogies can be more productively understood. The first of the three ideas is invariant measures on polyconvex sets. The authors then prove the fundamental lemma of integral geometry, namely the kinematic formula. Finally the analogues between invariant measures and finite partially ordered sets are investigated, yielding insights into Hecke algebras, Schubert varieties and the quantum world, as viewed by mathematicians. Geometers and combinatorialists will find this a most stimulating and fruitful story.



Topics In Integral Geometry


Topics In Integral Geometry
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Author : De-lin Ren
language : en
Publisher: World Scientific
Release Date : 1994

Topics In Integral Geometry written by De-lin Ren and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.


Essentials of integral geometry in a homogenous space are presented and the focus is on the basic results and applications. This book provides the readers with new findings, some being published for the first time and serves as an excellent graduate text.



Integral Geometry And Geometric Probability


Integral Geometry And Geometric Probability
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Author : Luis A. Santalo
language : en
Publisher: Cambridge University Press
Release Date : 1984-12-28

Integral Geometry And Geometric Probability written by Luis A. Santalo and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-12-28 with Mathematics categories.


Integral geometry originated with problems on geometrical probability and convex bodies. Its later developments, however, have proved to be useful in several fields ranging from pure mathematics (measure theory, continuous groups) to technical and applied disciplines (pattern recognition, stereology). This book is a systematic exposition of the theory and a compilation of the main results in the field. The volume can be used for a one-semester undergraduate course in probability and differential geometry or as a complement to classical courses on differential geometry, Lie groups, or probability.



Stochastic And Integral Geometry


Stochastic And Integral Geometry
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Author : Rolf Schneider
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-08

Stochastic And Integral Geometry written by Rolf Schneider and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-08 with Mathematics categories.


Stochastic geometry deals with models for random geometric structures. Its early beginnings are found in playful geometric probability questions, and it has vigorously developed during recent decades, when an increasing number of real-world applications in various sciences required solid mathematical foundations. Integral geometry studies geometric mean values with respect to invariant measures and is, therefore, the appropriate tool for the investigation of random geometric structures that exhibit invariance under translations or motions. Stochastic and Integral Geometry provides the mathematically oriented reader with a rigorous and detailed introduction to the basic stationary models used in stochastic geometry – random sets, point processes, random mosaics – and to the integral geometry that is needed for their investigation. The interplay between both disciplines is demonstrated by various fundamental results. A chapter on selected problems about geometric probabilities and an outlook to non-stationary models are included, and much additional information is given in the section notes.



Random Sets And Integral Geometry


Random Sets And Integral Geometry
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Author : Georges Matheron
language : en
Publisher: John Wiley & Sons
Release Date : 1974

Random Sets And Integral Geometry written by Georges Matheron and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Mathematics categories.




Geometric Probability


Geometric Probability
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Author : Herbert Solomon
language : en
Publisher: SIAM
Release Date : 1978-06-01

Geometric Probability written by Herbert Solomon and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978-06-01 with Mathematics categories.


Topics include: ways modern statistical procedures can yield estimates of pi more precisely than the original Buffon procedure traditionally used; the question of density and measure for random geometric elements that leave probability and expectation statements invariant under translation and rotation; and much more.



Factorization Calculus And Geometric Probability


Factorization Calculus And Geometric Probability
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Author : R. V. Ambartzumian
language : en
Publisher: Cambridge University Press
Release Date : 1990-09-28

Factorization Calculus And Geometric Probability written by R. V. Ambartzumian and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-09-28 with Mathematics categories.


The classical subjects of geometric probability and integral geometry, and the more modern one of stochastic geometry, are developed here in a novel way to provide a framework in which they can be studied. The author focuses on factorization properties of measures and probabilities implied by the assumption of their invariance with respect to a group, in order to investigate nontrivial factors. The study of these properties is the central theme of the book. Basic facts about integral geometry and random point process theory are developed in a simple geometric way, so that the whole approach is suitable for a nonspecialist audience. Even in the later chapters, where the factorization principles are applied to geometrical processes, the only prerequisites are standard courses on probability and analysis. The main ideas presented have application to such areas as stereology and geometrical statistics and this book will be a useful reference book for university students studying probability theory and stochastic geometry, and research mathematicians interested in this area.



An Introduction To Geometrical Probability


An Introduction To Geometrical Probability
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Author : A.M. Mathai
language : en
Publisher: CRC Press
Release Date : 1999-12-01

An Introduction To Geometrical Probability written by A.M. Mathai and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-12-01 with Mathematics categories.


A useful guide for researchers and professionals, graduate and senior undergraduate students, this book provides an in-depth look at applied and geometrical probability with an emphasis on statistical distributions. A meticulous treatment of geometrical probability, kept at a level to appeal to a wider audience including applied researchers who will find the book to be both functional and practical with the large number of problems chosen from different disciplines A few topics such as packing and covering problems that have a vast literature are introduced here at a peripheral level for the purpose of familiarizing readers who are new to the area of research.